Self-similar traffic generation

ABSTRACT

There is disclosed apparatus and methods for mimicking self-similar traffic in a telecommunications network. One ore more self-similar streams of data units may be generated according to values of selected parameters for the streams, such as the Hurst parameter. Values may be pre-calculated and stored in a table in a memory. To generate the stream, a traffic distribution is generated based on the values of the parameters, and through retrieval of the values from the table.

NOTICE OF COPYRIGHTS AND TRADE DRESS

[0001] A portion of the disclosure of this patent document containsmaterial which is subject to copyright protection. This patent documentmay show and/or describe matter which is or may become trade dress ofthe owner. The copyright and trade dress owner has no objection to thefacsimile reproduction by any one of the patent disclosure as it appearsin the Patent and Trademark Office patent files or records, butotherwise reserves all copyright and trade dress rights whatsoever.

BACKGROUND OF THE INVENTION

[0002] 1. Field of the Invention

[0003] The present invention relates to traffic generation for networkanalysis and network testing.

[0004] 2. Description of Related Art

[0005] Multiple recent studies of high-speed Ethernet, ATM, Local-AreaNetworks (LAN), Wide-Area Networks (WAN), Storage Area Networks (SAN)I/O traffic, signaling, WWW, multimedia and video traffic havedemonstrated that the variability in typical network traffic involvesnon-negligible correlations across several time-scales. Theseevaluations challenge traditional data traffic modeling, traditionallybased on the Poisson process and other Short-Range Dependent (SRD)processes.

[0006] One of the most striking features of packet-switched networktraffic is its tremendous burstiness, persistent at practically any timescale. Such Long-Range Dependence (LRD) manifests itself through aself-similar or fractal-like behavior. “Self-similarity” means that asegment of traffic measured at one time scale resembles an appropriatelyscaled version of the traffic at a different time scale.

[0007] Many networking studies have considered self-similarity, both foranalysis and synthesis of the fractal characteristics of networktraffic. The communications industry (e.g., AT&T, Nortel, Ericsson) hasbeen supportive of research groups in this area, and more recently somecompanies have started developing self-similar traffic generators tomeasure and test networking equipment, as well as properly scale itduring system design.

[0008] Fractal phenomena are common in both natural and human-madescenarios, including natural landscapes, ocean waves, earthquakedistributions, stock market behavior, and packet-network traffic. Asused herein, fractal and self-similar behavior are considered synonyms.

[0009] It has been proven that heavy tails in flow sizes (or lengths)are able to generate self-similarity. Heavy-tail distributions are thosewhose tails decay with a power law (which is a much slower decay thanexponential), indicating non-negligible probability even for extremelylarge observations. They describe long-memory processes with robust timedependence configurations that vanish very slowly. The“heavy-tailedness” of a random variable puts in evidence the combinationof numerous small observations mixed with a few large observations,where most of the contributions to the sample mean and variance of thedataset comes from the few large observations.

[0010] Important work in this field has been done by Leland, Taqqu,Willinger and Wilson. See, for example, W. E. Leland, M. S. Taqqu, W.Willinger, and D. V. Wilson, “A Bibliographical Guide to Self-SimilarTraffic and Performance Modeling for Modern High-Speed Networks,” inStochastic Networks, F. P. Kelly, S. Zachary, and I. Zieldins (eds.),Oxford University Press, pp. 339-366, 1996; and W. E. Leland, M. S.Taqqu, W. Willinger, and D. V. Wilson, “On the self-similar nature ofEthernet traffic,” IEEE/ACM Transactions on Networking, vol. 2, pp.1-14, February 1994. Other important work in the field has been done Seefor, example, B. K. Ryu, “Fractal Network Traffic: From Understanding toions,” Ph.D. Thesis, Columbia University, NY, 1996.

DESCRIPTION OF THE DRAWINGS

[0011]FIG. 1 is a block diagram of an environment in accordance with theinvention.

[0012]FIG. 2 is a block diagram of an apparatus according to one aspectof the invention.

[0013]FIG. 3 is a functional block diagram in accordance with theinvention.

[0014]FIG. 4 is a flow chart of a method in accordance with anotheraspect of the invention.

[0015]FIG. 5 is a state machine modeling a TCP flow in accordance withthe invention.

[0016]FIG. 6 is a graph of ON/OFF properties of a sample of TCP traffic.

DETAILED DESCRIPTION OF THE INVENTION

[0017] Throughout this description, the embodiments and examples shownshould be considered as exemplars, rather than limitations on theapparatus and methods of the present invention.

[0018] The superposition of multiple ON/OFF sources (also known as“packet trains”) with high variability and infinite variance results inan aggregate self-similar sequence (network traffic). Thereforeproducing and aggregating ON/OFF sources with heavy-tailed disributionsis a feasible approach for self-similar traffic generation. Theinvention, in one respect, uses the ability of aggregated heavy-taileddistributions to generate self-similar sequences. According to oneaspect of the invention, a traffic distribution is set to be heavytailed in the ON periods, the OFF periods, or both.

[0019] Multiplexing several independent and identically distributed(i.i.d.) heavy-tailed ON/OFF sources can generate self-similar traffic.Each ON state corresponds to the period when a packet train is beingtransmitted, and each OFF state corresponds to the quiescent periodbetween packet trains. Referring now to FIG. 5, there is shown a simplestate machine describing this basic structure. In state 510, a packettrain is sent. In state 520, there is a quiescent period between trains.FIG. 6 shows a schematic traffic plot, with sequences of ON periods whendata is being sent, followed by OFF periods of silence in between them.

[0020] ON/OFF heavy tailed distributions for traffic generation may beapplied in different ways. According to one aspect of the invention, asequence of natural numbers is generated that is self-similar, where themeaning of those integers is irrelevant from the generation point ofview. The integers may correspond to the number of packets, to thenumber of bytes per unit time (or specified time-bin), or to anythingelse. The use of the self-similar sequence is to be determined aposteriori.

[0021] There is abundant literature on several possible approaches togenerating self-similar sequences. Herein, aspects related to some ofthem are discussed. One approach employs the aggregation of competingTCP flows in the same channel. A second approach uses the aggregation ofseveral Pareto-distributed pseudo-random number generators into onemultiplexed output. A third approach uses truncated Paretodistributions. Each one or a combination may be utilized to produceself-similar sequences.

[0022] Competing TCP Flows: Controlling Chaos

[0023] Since TCP flows can be modeled as ON/OFF sources with heavy-taildistribution, competing TCP flows can be used to generate the desiredscaling structure of the traffic. By aggregating a collection ofcompeting TCP flows in the same channel, the chaotic mechanisms of TCPcan generate scaling behavior on large timescales.

[0024] TCP's congestion window size is one of the multiple aspects thatcharacterize the dynamics of competing “greedy” TCP flows on the samelink. Depending on a few parameters, such as link rate, buffer size, anddelay, the individual behavior of the flows is modified as well as theaggregated performance.

[0025] By artificially increasing congestion in the link or escalatingthe drop rate, the time-out mechanisms kick-in, increasing the silentperiods between packet trains, hence the OFF-periods become even moreheavy-tailed. The heaviest of the tails is the one that dominates howself-similar the resulting sequence will be, therefore by sufficientlyincreasing the OFF-periods the degree of self-similarity H can becontrolled. Notice that not all configurations of link rates, buffersizes, and delays generate self-similar time-series, and in some casesthey experience high sensitivity to initial conditions. It has beenreported that the ratio buffer size/delay seems to be what most directlycontrols the performance of the system. Larger loss rates tend to createlonger-timescale dependence in the generated traffic. Furthermore, ithas been verified that indeed “real” TCP micro-flows exhibit long-rangedependence when measured in real packet networks, as TCP connectionsover the Internet.

[0026] Artificially increasing congestion in the link may produceself-similar TCP traffic per-se. However, by exploiting the propertiesof the TCP end-to-end flow-control and congestion-avoidance mechanisms,a self-similar sequence may also be created. Such a sequence of valuesis simply the count of packets (or bytes, etc.) that “went through” thelink.

[0027] To generate specific types of TCP or other kinds of traffic, atraffic distribution may be used to modulate a stream. The minimumnumber of competing TCP flows needed to generate fractal behavior may beimplemented using two full TCP stacks talking to each other, undercertain loss-rate and other conditions. A pair of TCP stacks may be usedto create one self-similar sequence.

[0028] References relied upon for this discussion included: L. Guo, M.Crovella, I. Matta “How does TCP generate Pseudo-self-similarity?,” inProceedings of the International Workshop on Modeling, Analysis andSimulation of Computer and Telecommunications Systems—MASCOTS '01,Cincinnati, Ohio, August 2001; Veres and Boda, “The Chaotic Behavior ofTCP Congestion Control,” Proceedings of IEEE INFOCOM, Tel-Aviv, March2000; B. Sikdar and K. S. Vastola, “On the Contribution of TCP to theSelf-Similarity of Network Traffic,” lecture notes in computer science,Proceedings of IWDC, vol. 2170, pp. 596-613, 2001; and B. Sikdar and K.S. Vastola, “The Effect of TCP on the Self-Similarity of NetworkTraffic,” Proceeding of 35th Conference on Information Sciences andSystems, Baltimore, Md., March 2001.

[0029] Pareto Aggregation

[0030] In the Pareto aggregation approach, multiplexing severalindependent and identically distributed (i.i.d.) heavy-tailed ON/OFFsources can generate self-similar traffic.

[0031] The simplest heavy-tailed distribution is the Paretodistribution, which for a random variable X has a probability massfunction (pmf)${{p(x)} = {{\alpha \quad b^{\alpha}x^{{- \alpha} - 1}} = \frac{\alpha \quad b^{\alpha}}{x^{\alpha + 1}}}},$

[0032] with α,b>0 and x>b, where α is the shape parameter or tail indexand b is the minimum possible value of X. The corresponding cumulativedistribution function (cdf) is${F(x)} = {{P\left\lbrack {X \leq x} \right\rbrack} = {1 - {\left( \frac{b}{x} \right)^{\alpha}.}}}$

[0033] A collection of ON/OFF Pareto engines may be used, each based onan independent Pseudo-Random Number Generator (PRNG). EveryPareto-distributed sequence can be implemented as${X_{Pareto} = \frac{b}{U^{1/\alpha}}};{0 < U \leq 1}$${\log_{2}X_{Pareto}} = {{\log_{2}b} - {\frac{1}{\alpha}\log_{2}U}}$$X_{Pareto} = 2^{\log_{2}b\frac{1}{\alpha}\log_{2}U}$

[0034] where U is a uniformly distributed random variable.

[0035] For self-similar traffic 1≦α≦2, where the lower the value of α,the higher the probability of very large values of X Notice that forα≦2, then X has an infinite variance, and for α≦1, then X has aninfinite mean.

[0036] The relationship between the shape parameter α and the degree ofself-similarity, given by the Hurst parameter H, is$H = {\frac{3 - \alpha}{2}.}$

[0037] References relied upon for this discussion included: W.Willinger, M. S. Taqqu, R. Sherman, and D. Wilson, “Self-SimilarityThrough High-Variability: Statistical Analysis of Ethernet LAN Trafficat the Source Level,” proceedings of the ACM SIGCOMM '95, pp 100-113,Cambridge Mass., August 1995; W. Willinger, M. S. Taqqu, R. Sherman, andD. Wilson, “Self-Similarity Through High-Variability: StatisticalAnalysis of Ethernet LAN Traffic at the Source Level,” IEEE/ACM Trans onNetworking 5:71-86, 1997; L. G. Samuel, J. M. Pitts, R. J. Mondragón,“Fast Self-Similar Traffic Generation,” Proceedings of the Fourteenth UKTeletraffic Symposium on Performance Engineering in Information Systems,Manchester UK, March 1997, pp 8/1-8/4; G. Kramer, B. Mukherjee, and G.Pesavento, “Interleaved Polling with Adaptive Cycle Time (IPACT): ADynamic Bandwidth Distribution Scheme in an Optical Access Network,”Photonic Network Communications, Volume 4 (1), January 2002. Pages89-107; M. E. Crovella and L. Lipsky, “Long-Lasting Transient Conditionsin Simulations with Heavy-Tailed Workloads,” Proceedings of the 1997Winter Simulation Conference (WSC-97), December 1997; and J. Wallerich,“Self-Similarity and Heavy Tailed Distributions, Design andImplementation of a WWW Workload Generator for the NS-2 NetworkSimulator” (Chapter 2.2), NSWEB.

[0038] Truncated-Value Pareto Distributions

[0039] In accordance with one aspect of the invention, truncated-valuePareto distributions may be generated by selecting a minimum length ofthe OFF period for every Pareto ON/OFF source i. This may be achieved byassuming a given packet size k, a given load L_(i) for each source, andthe shape parameters (a.k.a. tail indices) α_(ON) and α_(OFF) for theON-period and OFF-period respectively. Note that the minimum length ofthe ON period is one packet, M_(ON)=1. The duration of the minimumlength for the OFF period for source i is${M_{OFF} = {k \times \frac{T_{OFF}}{T_{ON}} \times \frac{1 - S^{T_{ON}}}{1 - S^{T_{OFF}}} \times \left( {\frac{1}{L_{i}} - 1} \right)}},$

[0040] denoting${T_{ON} = {{\frac{\alpha_{ON} - 1}{\alpha_{ON}}\quad {and}\quad T_{OFF}} = \frac{\alpha_{OFF} - 1}{\alpha_{OFF}}}},$

[0041] and where S is the smallest non-zero value that the uniform PRNGcan produce.

[0042] When using a finite precision system, e.g., a computer, togenerate a pseudo-Pareto distribution with the above M_(OFF) minimumOFF-time there will be a higher density of points toward the lower-endof the scale. Regardless of the window size, toward the tail end of thedistribution there will always be a region where the distance betweentwo points with non-zero probability exceeds an arbitrarily chosenwindow size. The undesired consequence is that some windows will containno samples, even when the total number of samples asymptotically tendsto infinity. This introduces error in the mean size of the ON and OFFperiods is due to the discrete nature of the implementation versus thecontinuous nature of the theoretical Pareto distribution. A heuristicsolution, using a correction coefficient C, leads to$M_{OFF} = {k \times \frac{C_{ON}}{C_{OFF}} \times \frac{T_{OFF}}{T_{ON}} \times \frac{1 - S^{T_{ON}}}{1 - S^{T_{OFF}}} \times {\left( {\frac{1}{L_{i}} - 1} \right).}}$

[0043] The lengths of the ON and OFF periods may be regulated byadjusting the α_(ON) and α_(OFF) parameters. Arguably, α_(ON)>α_(OFF)for real traffic, since usually the probability of a very large OFFperiod is higher than the probability of an equally large ON period.

[0044] Given C=(1.19α−1.166)^(−0.027) as a heuristic correctioncoefficient, and if α_(ON)=α_(OFF) is chosen, then the expression forM_(OFF) appreciably reduces to$M_{OFF} = {k \times {\left( {\frac{1}{L_{i}} - 1} \right).}}$

[0045] Since (1/α) and (log₂b) are constant, then the only calculationof table look-up operation needed is for (log₂U).

[0046] References relied upon for this discussion included: G. Kramer,“On Generating Self-Similar Traffic Using Pseudo-Pareto Distribution,”Tutorial, U. C. Davis.

[0047] The implementation of the exponentials (of base-2), to execute2^(1/αlog) ₂ ^(U) as part of the culcation of the X_(Pareto), is quitesimple for integer exponents. The same simple method may be used forfloating point exponents with minor modifications. Choosing base-2 makesthe calculation of 2^(j) to be simply a “set-to-1” operation of the(binary) bit placed at the j^(th) (in order of increasing significance,starting with j=0 on the right-hand-side).

[0048] This approach may be applied for floating point exponents byincluding the point in the binary representation of the exponent andadjusting the bit to be set to one accordingly, for example.

[0049] Pseudo random numbers may be first generated with a uniformlydistributed PRNG, and then shaped as Pareto using the above equations,implemented in a table. Having a resolution in the table below thenumber of potentially different number of inputs to the table (theUniform values) would mean that some end up getting mapped to the sameoutput value. Therefore, it is necessary to have a resolution given bythe self-similar maximum length, and the desired granularity.

[0050] It is not strictly necessary to generate heavy-taileddistributions for both the ON and the OFF periods. Generating one heavytail distribution may be adequate, and the other one can have anotherdistribution. For example, a random time (between some boundaries) maybe used for one type of period (ON or OFF), and the other may bePareto-distributed.

[0051] Description of the System

[0052] Referring now to FIG. 1, there is shown a block diagram of anenvironment in accordance with the invention. The environment includes atraffic generator 100, a network 140 and plural network devices 150.

[0053] The traffic generator 100 may be a network testing device,performance analyzer, conformance validation system, network analyzer,network management system, or programmed general purpose computer (e.g.,a PC). The traffic generator 100 may include one or more network cards120 and a back plane 110. Traffic generator 100 may be in the form of acard rack, as shown in FIG. 1, or may be an integrated unit.Alternatively, the traffic generator may comprise a number of separateunits cooperative to provide traffic generation. The traffic generator100 and the network cards 120 may support one or more well knownstandards or protocols such as the 10 Gigabit Ethernet and Fibre Channelstandards, and may support proprietary protocols as well.

[0054] The network cards 120 may include one or more field programmablegate arrays (FPGA), application specific integrated circuits (ASIC),programmable logic devices (PLD), programmable logic arrays (PLA),processors and other kinds of devices. In addition, the network cards120 may include software and firmware. The term network card encompassesline cards, test cards, analysis cards, network line cards, loadmodules, interface cards, network interface cards, data interface cards,packet engine cards, service cards, smart cards, switch cards, relayaccess cards, and the like. Each network card 120 may provide one ormore network ports. The ports of the network cards 120 may be connectedto the network through wire, optical fiber, wirelessly or otherwise.Each network card 120 may support a single communications protocol, maysupport a number of related protocols, or may support a number ofunrelated protocols. The network cards 120 may be permanently installedin the traffic generator 100 or field removable. Each network card 120may provide one or more ports.

[0055] The back plane 110 may serve as a bus or communications mediumfor the network cards 120. The back plane 110 may also provide power tothe network cards 120.

[0056] The network devices 150 may be any devices capable ofcommunicating over the network 140. The network devices 150 may becomputing devices such as workstations, personal computers, servers,portable computers, personal digital assistants (PDAs), computingtablets, and the like; peripheral devices such as printers, scanners,facsimile machines and the like; network capable storage devicesincluding disk drives such as network attached storage (NAS) and storagearea network (SAN) devices; networking devices such as routers, relays,hubs, switches, bridges, and multiplexers. In addition, the networkdevices 150 may include appliances such as refrigerators, washingmachines, and the like as well as residential or commercial HVACsystems, alarm systems, and any other device or system capable ofcommunicating over a network.

[0057] The network 140 may be a LAN, a WAN, a SAN, wired, wireless, or acombination of these, and may include or be the Internet. Communicationson the network 140 may take various forms, including frames, cells,datagrams, packets or other units of information, all of which arereferred to herein as data units. The traffic generator 100 and thenetwork devices 150 may communicate simultaneously with one another, andthere may be plural logical communications between the traffic generator100 and a given network device 150. The network itself may be comprisedof numerous nodes providing numerous physical and logical paths for datato travel.

[0058] A flow of data units originating from a single source on thenetwork having a specific type of data unit and a specific rate will bereferred to herein as a “stream.” A source may support multiple outgoingand incoming streams simultaneously and concurrently, for example toaccommodate multiple data unit types or rates. A source may be, forexample, a port on a network interface. “Simultaneously” means “atexactly the same time.” “Concurrently” means “within the same time.” Asingle stream may represent one or more concurrent “sessions.” A“session” is a lasting connection between a fixed, single source, and afixed, single destination comprising a sequence of one or more dataunits. The sessions within a stream share the data rate of the streamthrough interleaving. The interleaving may be balanced, unbalanced, anddistributed among the represented sessions. Two or more sessionsrepresented by the same stream may transmit data units from a sourceconcurrently, but not simultaneously.

[0059] Although a session carries data units between two fixed endpoints, the session may include multiple paths within the network 140.Within the network 140, sessions may be broken apart and reconstitutedto allow for greater data rates, better error control, better networkutilization, lower costs or otherwise. The sessions may include one ormore intermediary paths, channels, or routes between one or moreintermediary devices. The multiple intermediary paths, channels orroutes may be aligned in parallel and/or serially with respect to oneanother within the network 140.

[0060] Referring now to FIG. 2, there is shown a block diagram of anapparatus according to one aspect of the invention. The apparatus may bethe traffic generator 100 (FIG. 1), the network card 120 (FIG. 1), orone or more components of the traffic generator 100 (FIG. 1) or thenetwork card 120 (FIG. 1), such as a port. The apparatus includes acontrol unit 210, a blaster unit 240, a receive engine 220, a frontend/transmit engine 250, a bus 230 and communication paths 260, 265.

[0061] The bus 230 provides a communications path between the controlunit 210, the receive engine 220, the blaster unit 240, the frontend/transmit engine 250 and the back plane 110. The bus 230 may be usedfor communicating control and status information, and also data.Communication paths 260, 265 may be used for communicating data, andalso control and status information.

[0062] The control unit 210 includes a port processor 212, a DMA engine214, and a port memory 216. The control unit 210 may provide PRNG.

[0063] The port processor 212 may be a microprocessor or otherprogrammable processor. From outside the apparatus, the port processor212 receives control instructions such as patterns of traffic which theapparatus is to generate. The control instructions may be received froma network device over an incoming stream 222. Alternatively, the controlinstructions may be provided directly to the apparatus via the bus 230,for example via the back plane 110. The port processor 212 may have anapplication program interface (API) for external control of theapparatus. A user may use a software program on a host to enter commandswhich create the control instructions that are sent to the portprocessor 212. The control unit 210 may store the control instructionsin port memory 216 before, after, and during their execution.

[0064] The DMA engine 214 comprises an interface and control logicproviding demand memory access. The DMA engine 214 is coupled to theport processor 212, the port memory 216, the receive engine 220 and thebus 230. In response to requests from the port processor 212, the DMAengine 214 fetches data units and data from the port memory 216. The DMAengine 214 also provides a path from the port processor 212 to theblaster unit 240 and the front end/transmit engine 250.

[0065] The receive engine 220 receives incoming data streams, such asstream 222. The incoming stream 222. The receive engine 220 may processincoming data units according to a filter provided by or controlled bythe port processor 212. After receiving the incoming data units, thereceive engine 220 passes the data units to the DMA engine 214, whichmay store the data units in the port memory 216 or pass them directly tothe port processor 212. The receive engine may communicate with the DMAengine 214 via bus 230 and/or communication line 265. Incoming dataunits may also be discarded, for example by either the receive engine220 (e.g., filtered out) or the DMA engine 214. Incoming data units mayinclude control data from a network device, e.g., for negotiating,setting up, tearing down or controlling a session. Incoming data unitsmay also include data from a network device.

[0066] The front end/transmit engine 250 transmits outgoing data unitsas one or more streams 252 a, 252 b, . . . 252 n. The data units, whichthe front end/transmit engine 250 transmits, may originate from thecontrol unit 210 or the blaster unit 240. The control unit 210originates control data for negotiating, setting up, tearing down andcontrolling streams and sessions. The front end/transmit engine 250 iscoupled to the bus 230 and communications line 265 for receiving controlinformation and data units.

[0067] The blaster unit 240 includes a scheduler 242, a backgroundoverlay engine 244, a background memory 246, an overlay memory 248, anda front end/transmit engine 250. The scheduler 242, the backgroundoverlay engine 244 and the background memory 246 cooperate to form dataunits and to pass these data units to the front end/transmit engine 250.

[0068] The blaster unit 240 uses session configuration information,comprising instructions for forming and timing transmission of theoutgoing data units. The blaster unit 240 may receive the sessionconfiguration information from the port processor 212. The components ofthe session configuration information may be communicated as a unit orseparately.

[0069] At least some of the session configuration information—templatesand overlays—may be stored in the two memories 246, 248 of the blasterunit 240. The background memory 246 stores a template for the data unitsof each outgoing stream 252. The overlay memory 248 stores an overlayfor each outgoing session 254. Whereas the template provides a basiclayout of what will be an outgoing data unit, the overlay memory 248dictates how the template will be modified or completed to produce thedata units of the session. Although the overlay memory 248 and thebackground memory 246 are shown as separate units, they may be combinedinto a single memory. Likewise, the port memory 216 may be combined withone or both of the background memory 246 and the overlay memory 248.

[0070] The scheduler 242 manages a schedule of transmission times foreach of the outgoing streams, such as streams 252 a, 252 b, 252 n. Thescheduler 242 operates like a metronome or clock to ensure that theoutgoing streams conform to their respective data rates. Once configuredand enabled for a given stream, the scheduler 242 sends a next transmitsignal to the background overlay engine 244 when a data unit for thecorresponding stream is to be transmitted. Alternatively, the scheduler242 may signal to the background overlay engine 244 when the backgroundoverlay engine 244 should form an outgoing data unit, and the backgroundoverlay engine 244 implicitly passes the formed data units to the frontend/transmit engine 250 for transmission. The scheduler 242 is connectedto the bus 230 is coupled to the bus 230 for receiving controlinformation.

[0071] The background overlay engine 244 forms outgoing data units. Thebackground overlay engine 244 is coupled to the scheduler 242, thebackground memory 246, the overlay memory 248 and the front end/transmitengine 250. The background overlay engine 244 uses the templates in thebackground memory 246 and overlays in the overlay memory 248, combiningthem to form outgoing data units. When signaled by the scheduler 242,the background overlay engine 244 passes a formed outgoing data unit fora session of the signaled stream to the front end/transmit unit 250.

[0072] Referring now to FIG. 3, there is shown a functional blockdiagram in accordance with the invention. The diagram includes a buffer310, an arbitrator 320, tables 340, a distribution calculator 330 and ascheduler 350.

[0073] The buffer 310 may comprise plural shift registers, a memory, orother device. The buffer 310 receives self-similarity parameters for thestreams to be generated. These parameters may include the Hurstparameter, and may correspond to the ON or OFF period for thecorresponding stream.

[0074] The arbitrator 320 comprises logic for selecting at least one ofthe streams to service next. The number of streams which may be selectedmay be dependent on the processing and/or logic capabilities of thearbitrator 320 and other components.

[0075] The tables 340 store distributed sequences for self-similartraffic. The tables 340 may be stored in a memory. These distributedsequences may correlate to a range of values for the Hurst parameter.

[0076] The distribution calculator 330 comprises logic for generating aself-similar traffic distribution for the selected stream based on theself similarity parameters for the selected stream. The distributioncalculator 330 retrieves a distributed sequence (or other values asdescribed herein) from the tables 340 based upon the self-similarityparameters for the selected stream. The distribution calculator 330produces the traffic distribution for the stream according to a formulawhich uses the retrieved distributed sequence.

[0077] According to one aspect of the invention, the self-similartraffic distribution is based upon distributed sequences described by aformula having a shape parameter, a minimum value for the respectivedistributed sequence and a uniformly distributed random variable. Theshape parameter has a fixed value. The minimum value for the distributedsequences is fixed. The tables 340 store logarithms of values of theuniformly distributed random variable.

[0078] The scheduler 350 may be the scheduler 242 (FIG. 2). Thescheduler 350 may allocate rate for each packet within a train, withoutoverflowing packets to any later ON (or OFF) periods. The scheduler 350may incorporate some notion of duration of the packets.

[0079] Description Of The Methods

[0080] Referring now to FIG. 4, there is shown a flow chart of a methodin accordance with other aspect of the invention. As a preliminarymatter, it may be desirable or necessary to select a particular formulafor generating the self-similar traffic distributions. Furthermore, itmay be desirable or necessary to pre-calculate distributed sequences orother values for storage in the tables or memory. Finally, it may bedesirable or necessary to store the pre-calculated distributed sequencesor other values for storage in the tables or memory. The tables ormemory may store distributed sequences for self-similar trafficcorrelated to a range of values for the Hurst parameter and/or otherparameters. The stored values may be logarithms of values of a uniformlydistributed random integer.

[0081] These steps may be performed at the start of the method (step405), although they may also be performed subsequent to the start (step405). Thus, the formula and pre-calculations may be dynamically changedduring the course of traffic generation. In this way, different patternsor degrees of self-similarity may be obtained.

[0082] In performing the method, one step is to provide values for atleast one self-similarity parameter for the streams (step 410). Theself-similarity parameters may include the Hurst parameter, an averagearrival time and a fractal onset time.

[0083] If all streams are generated, (step 425), then no furtherprocessing is necessary (step 495).

[0084] In another step, a next stream is selected (step 430). More thanone stream may be selected, for example for processing in a pipelined orparallel manner.

[0085] Next, a distribution is generated for the selected streams (step435). The self-similar traffic distributions may be based upondistributed sequences retrieved from memory or the tables 340 (FIG. 3).The value of the Hurst parameter for the respective streams may alone beused to retrieve the distributions. The values of the average arrivaltime, the fractal onset time, and or other parameters may be used forretrieving the distributed sequences from the table 340 (FIG. 3), inconjunction with the Hurst parameter. The retrieved values may be thepre-calculated logarithms.

[0086] As described above, the distributed sequences may be described bymany different approaches. For example, the distributed sequences maycomprise superposition of plural independent and probabilisticallyidentical fractal renewal processes. The distributed sequences may bedescribed by a formula having a shape parameter and a minimum value forthe respective distributed sequence and a uniformly distributed randomvariable. The value for the shape parameter may be fixed and the minimumvalue for the distributed sequences may be fixed. If so, then the tables340 (FIG. 3) may comprise logarithms of values of the uniformlydistributed random variable.

[0087] After the distribution is generated for the selected streams, theselected streams may be generated (step 440). Steps 430, 435 and 440repeat until all the streams have been generated (step 425), unless ofcourse the process is interrupted. The generated streams of self-similartraffic may then be applied to a portion of a telecommunicationsnetwork. The generated streams may also be used to simulate a behaviorof a portion of the telecommunications network.

[0088] Although exemplary embodiments of the present invention have beenshown and described, it will be apparent to those having ordinary skillin the art that a number of changes, modifications, or alterations tothe invention as described herein may be made, none of which depart fromthe spirit of the present invention. All such changes, modifications andalterations should therefore be seen as within the scope of the presentinvention.

It is claimed:
 1. A method for mimicking self-similar traffic in atelecommunications network, the method comprising providing a table ofdistributed sequences for self-similar traffic providing values for atleast one self-similarity parameter for plural streams, theself-similarity parameters including a Hurst parameter selecting atleast one of the streams generating a self-similar traffic distributionfor the selected streams based on the values of the self similarityparameters for the selected streams, wherein the self-similar trafficdistribution is further based upon distributed sequences retrieved fromthe table based upon the value of the Hurst parameter for the selectedstreams.
 2. The method for mimicking self-similar traffic in atelecommunications network of claim 1, wherein the distributed sequencesare Pareto-distributed sequences.
 3. The method for mimickingself-similar traffic in a telecommunications network of claim 1, whereinthe distributed sequences are truncated-value Pareto distributions. 4.The method for mimicking self-similar traffic in a telecommunicationsnetwork of claim 1, wherein the distributed sequences comprise competingflows.
 5. The method for mimicking self-similar traffic in atelecommunications network of claim 4 wherein the distributed sequenceseach comprise a single ON/OFF process.
 6. The method for mimickingself-similar traffic in a telecommunications network of claim 1, whereinthe traffic distribution comprises a series of ON and OFF periods. 7.The method for mimicking self-similar traffic in a telecommunicationsnetwork of claim 6, wherein only one of the ON and OFF periods has aheavy-tailed distribution.
 8. The method for mimicking self-similartraffic in a telecommunications network of claim 7, wherein theheavy-tailed distribution is a Pareto distribution.
 9. The method formimicking self-similar traffic in a telecommunications network of claim1 wherein the distributed sequences are described by a formula having ashape parameter and a minimum value for the respective distributedsequence and a uniformly distributed random variable.
 10. The method formimicking self-similar traffic in a telecommunications network of claim9 wherein the value for the shape parameter is fixed and the minimumvalue for the distributed sequences is fixed.
 11. The method formimicking self-similar traffic in a telecommunications network of claim10 wherein the table comprises logarithms of values of the uniformlydistributed random variable.
 12. The method for mimicking self-similartraffic in a telecommunications network of claim 1 wherein thedistributed sequences comprise superposition of plural independent andprobabilistically identical fractal renewal processes.
 13. The methodfor mimicking self-similar traffic in a telecommunications network ofclaim 1, wherein the self-similarity parameters include an averagearrival time and a fractal onset time.
 14. The method for mimickingself-similar traffic in a telecommunications network of claim 13 whereinthe values of the average arrival time and the fractal onset time areused for retrieving the distributed sequences from the table inconjunction with the Hurst parameter.
 15. The method for mimickingself-similar traffic in a telecommunications network of claim 1 furthercomprising generating the selected streams from the self-similar trafficdistribution.
 16. The method for mimicking self-similar traffic in atelecommunications network of claim 15 further comprising applying thegenerated streams of self-similar traffic to a portion of atelecommunications network.
 17. The method for mimicking self-similartraffic in a telecommunications network of claim 16 further comprisingsimulating a behavior of the portion of the telecommunications networkbased on the applied streams of self-similar traffic.
 18. A method formimicking self-similar traffic in a telecommunications network, themethod comprising providing values for at least one self-similarityparameter for plural streams, the self-similarity parameters including aHurst parameter selecting at least one of the streams generating aself-similar traffic distribution for the selected streams based on thevalues of the self similarity parameters for the selected streams,wherein the self-similar traffic distribution is further based upondistributed sequences retrieved from a memory based upon the value ofthe Hurst parameter for the selected streams, wherein the memory storesdistributed sequences for self-similar traffic correlated to a range ofvalues for the Hurst parameter.
 19. The method for mimickingself-similar traffic in a telecommunications network of claim 18,wherein the distributed sequences are Pareto-distributed sequences. 20.The method for mimicking self-similar traffic in a telecommunicationsnetwork of claim 18, wherein the distributed sequences aretruncated-value Pareto distributions.
 21. The method for mimickingself-similar traffic in a telecommunications network of claim 18,wherein the distributed sequences comprise competing flows.
 22. Themethod for mimicking self-similar traffic in a telecommunicationsnetwork of claim 21 wherein the distributed sequences each comprise asingle ON/OFF process.
 23. The method for mimicking self-similar trafficin a telecommunications network of claim 18, wherein the trafficdistribution comprises a series of ON and OFF periods.
 24. The methodfor mimicking self-similar traffic in a telecommunications network ofclaim 23, wherein only one of the ON and OFF periods has a heavy-taileddistribution.
 25. The method for mimicking self-similar traffic in atelecommunications network of claim 24, wherein the heavy-taileddistribution is a Pareto distribution.
 26. The method for mimickingself-similar traffic in a telecommunications network of claim 18 whereinthe distributed sequences are described by a formula having a shapeparameter and a minimum value for the respective distributed sequenceand a uniformly distributed random variable.
 27. The method formimicking self-similar traffic in a telecommunications network of claim26 wherein the value for the shape parameter is fixed and the minimumvalue for the distributed sequences is fixed.
 28. The method formimicking self-similar traffic in a telecommunications network of claim27 wherein the memory stores logarithms of values of the uniformlydistributed random variable.
 29. The method for mimicking self-similartraffic in a telecommunications network of claim 18 wherein thedistributed sequences comprise superposition of plural independent andprobabilistically identical fractal renewal processes.
 30. The methodfor mimicking self-similar traffic in a telecommunications network ofclaim 18, wherein the self-similarity parameters include an averagearrival time and a fractal onset time.
 31. The method for mimickingself-similar traffic in a telecommunications network of claim 30 whereinthe values of the average arrival time and the fractal onset time areused for retrieving the distributed sequences from the memory inconjunction with the Hurst parameter.
 32. The method for mimickingself-similar traffic in a telecommunications network of claim 18 furthercomprising generating the selected streams from the self-similar trafficdistribution.
 33. The method for mimicking self-similar traffic in atelecommunications network of claim 32 further comprising applying thegenerated streams of self-similar traffic to a portion of atelecommunications network.
 34. The method for mimicking self-similartraffic in a telecommunications network of claim 33 further comprisingsimulating a behavior of the portion of the telecommunications networkbased on the applied streams of self-similar traffic.
 35. A method formimicking self-similar traffic in a telecommunications network, themethod comprising providing values for at least one self-similarityparameter for plural streams, the self-similarity parameters including aHurst parameter selecting at least one of the streams generatingself-similar traffic distributions for the selected streams based thevalues of on the self similarity parameters for the selected streams,wherein the self-similar traffic distribution is based upon distributedsequences described by a formula having a shape parameter, a minimumvalue for the respective distributed sequences and a uniformlydistributed random variable the shape parameter has a fixed value theminimum value for the distributed sequences is fixed the distributedsequences are obtained from logarithms of values of the uniformlydistributed random variable.
 36. The method for mimicking self-similartraffic in a telecommunications network of claim 35 further comprisingpre-storing the logarithms of values of the uniformly distributed randomvariable in a memory in the generating step, obtaining the logarithmsfrom the memory.
 37. The method for mimicking self-similar traffic in atelecommunications network of claim 35 further comprising pre-storingthe distributed sequences in a memory in the generating step, obtainingthe distributed sequences from the memory.
 38. The method for mimickingself-similar traffic in a telecommunications network of claim 35,wherein the distributed sequences are Pareto-distributed sequences. 39.The method for mimicking self-similar traffic in a telecommunicationsnetwork of claim 35, wherein the distributed sequences aretruncated-value Pareto distributions.
 40. The method for mimickingself-similar traffic in a telecommunications network of claim 35,wherein the distributed sequences comprise competing flows.
 41. Themethod for mimicking self-similar traffic in a telecommunicationsnetwork of claim 40 wherein the distributed sequences each comprise asingle ON/OFF process.
 42. The method for mimicking self-similar trafficin a telecommunications network of claim 35, wherein the trafficdistribution comprises a series of ON and OFF periods.
 43. The methodfor mimicking self-similar traffic in a telecommunications network ofclaim 42, wherein only one of the ON and OFF periods has a heavy-taileddistribution.
 44. The method for mimicking self-similar traffic in atelecommunications network of claim 43, wherein the heavy-taileddistribution is a Pareto distribution.
 45. The method for mimickingself-similar traffic in a telecommunications network of claim 35 whereinthe distributed sequences comprise superposition of plural independentand probabilistically identical fractal renewal processes.
 46. Themethod for mimicking self-similar traffic in a telecommunicationsnetwork of claim 35, wherein the self-similarity parameters include anaverage arrival time and a fractal onset time.
 47. The method formimicking self-similar traffic in a telecommunications network of claim46 wherein the values of the average arrival time and the fractal onsettime are used for retrieving the distributed sequences from the memoryin conjunction with the Hurst parameter.
 48. The method for mimickingself-similar traffic in a telecommunications network of claim 35 furthercomprising generating the selected streams from the self-similar trafficdistribution.
 49. The method for mimicking self-similar traffic in atelecommunications network of claim 48 further comprising applying thegenerated streams of self-similar traffic to a portion of atelecommunications network.
 50. The method for mimicking self-similartraffic in a telecommunications network of claim 49 further comprisingsimulating a behavior of the portion of the telecommunications networkbased on the applied streams of self-similar traffic.
 51. An apparatusfor mimicking self-similar traffic in a telecommunications network, theapparatus comprising a buffer to receive values for at least oneself-similarity parameter for plural streams, the self-similarityparameters including a Hurst parameter an arbitrator coupled to thebuffer to select at least one of the streams a memory storing a table ofdistributed sequences for self-similar traffic a distribution calculatorcoupled to the memory, the distribution calculator to generate aself-similar traffic distribution for the selected streams based on thevalues of the self similarity parameters for the selected streams,wherein the self-similar traffic distribution is further based upondistributed sequences retrieved from the table based upon the value ofthe Hurst parameter for the selected streams a scheduler coupled to thedistribution calculator to schedule transmission of data units for theselected streams.
 52. The apparatus for mimicking self-similar trafficin a telecommunications network of claim 51, wherein the distributedsequences are Pareto-distributed sequences.
 53. The apparatus formimicking self-similar traffic in a telecommunications network of claim51, wherein the distributed sequences are truncated-value Paretodistributions.
 54. The apparatus for mimicking self-similar traffic in atelecommunications network of claim 51, wherein the distributedsequences comprise competing flows.
 55. The apparatus for mimickingself-similar traffic in a telecommunications network of claim 54 whereinthe distributed sequences each comprise a single ON/OFF process.
 56. Theapparatus for mimicking self-similar traffic in a telecommunicationsnetwork of claim 51, wherein the traffic distribution comprises a seriesof ON and OFF periods.
 57. The apparatus for mimicking self-similartraffic in a telecommunications network of claim 56, wherein only one ofthe ON and OFF periods has a heavy-tailed distribution.
 58. Theapparatus for mimicking self-similar traffic in a telecommunicationsnetwork of claim 57, wherein the heavy-tailed distribution is a Paretodistribution.
 59. The apparatus for mimicking self-similar traffic in atelecommunications network of claim 51 wherein the distributed sequencesare described by a formula having a shape parameter and a minimum valuefor the respective distributed sequence and a uniformly distributedrandom variable.
 60. The apparatus for mimicking self-similar traffic ina telecommunications network of claim 59 wherein the value for the shapeparameter is fixed and the minimum value for the distributed sequencesis fixed.
 61. The apparatus for mimicking self-similar traffic in atelecommunications network of claim 60 wherein the table compriseslogarithms of values of the uniformly distributed random variable. 62.The apparatus for mimicking self-similar traffic in a telecommunicationsnetwork of claim 51 wherein the distributed sequences comprisesuperposition of plural independent and probabilistically identicalfractal renewal processes.
 63. The apparatus for mimicking self-similartraffic in a telecommunications network of claim 51, wherein theself-similarity parameters include an average arrival time and a fractalonset time.
 64. The apparatus for mimicking self-similar traffic in atelecommunications network of claim 63 wherein the values of the averagearrival time and the fractal onset time are used for retrieving thedistributed sequences from the table in conjunction with the Hurstparameter.
 65. The apparatus for mimicking self-similar traffic in atelecommunications network of claim 51 further comprising a blaster unitto generate the selected streams from the self-similar trafficdistribution.
 66. The apparatus for mimicking self-similar traffic in atelecommunications network of claim 65 wherein the blaster unit includesthe scheduler.
 67. The apparatus for mimicking self-similar traffic in atelecommunications network of claim 65 further comprising a transmitengine to apply the generated streams of self-similar traffic to aportion of a telecommunications network.
 68. A network card comprisingthe apparatus of claim
 51. 69. A traffic generator comprising theapparatus of claim
 51. 70. An apparatus for mimicking self-similartraffic in a telecommunications network, the apparatus comprising abuffer to receive values for at least one self-similarity parameter forplural streams, the self-similarity parameters including a Hurstparameter an arbitrator coupled to the buffer to select at least one ofthe streams a memory storing distributed sequences for self-similartraffic correlated to a range of values for the Hurst parameter adistribution calculator coupled to the memory, the distributioncalculator to generate a self-similar traffic distribution for theselected streams based on the values of the self similarity parametersfor the selected streams, wherein the self-similar traffic distributionis further based upon distributed sequences retrieved from the memorybased upon the value of the Hurst parameter for the selected streams ascheduler coupled to the distribution calculator to scheduletransmission of data units for the selected streams.
 71. The apparatusfor mimicking self-similar traffic in a telecommunications network ofclaim 70, wherein the distributed sequences are Pareto-distributedsequences.
 72. The apparatus for mimicking self-similar traffic in atelecommunications network of claim 70, wherein the distributedsequences are truncated-value Pareto distributions.
 73. The apparatusfor mimicking self-similar traffic in a telecommunications network ofclaim 70, wherein the distributed sequences comprise competing flows.74. The apparatus for mimicking self-similar traffic in atelecommunications network of claim 70 wherein the distributed sequenceseach comprise a single ON/OFF process.
 75. The apparatus for mimickingself-similar traffic in a telecommunications network of claim 70,wherein the traffic distribution comprises a series of ON and OFFperiods.
 76. The apparatus for mimicking self-similar traffic in atelecommunications network of claim 75, wherein only one of the ON andOFF periods has a heavy-tailed distribution.
 77. The apparatus formimicking self-similar traffic in a telecommunications network of claim76, wherein the heavy-tailed distribution is a Pareto distribution. 78.The apparatus for mimicking self-similar traffic in a telecommunicationsnetwork of claim 70 wherein the distributed sequences are described by aformula having a shape parameter and a minimum value for the respectivedistributed sequence and a uniformly distributed random variable. 79.The apparatus for mimicking self-similar traffic in a telecommunicationsnetwork of claim 78 wherein the value for the shape parameter is fixedand the minimum value for the distributed sequences is fixed.
 80. Theapparatus for mimicking self-similar traffic in a telecommunicationsnetwork of claim 79 wherein the memory stores logarithms of values ofthe uniformly distributed random variable.
 81. The apparatus formimicking self-similar traffic in a telecommunications network of claim70 wherein the distributed sequences comprise superposition of pluralindependent and probabilistically identical fractal renewal processes.82. The apparatus for mimicking self-similar traffic in atelecommunications network of claim 70, wherein the self-similarityparameters include an average arrival time and a fractal onset time. 83.The apparatus for mimicking self-similar traffic in a telecommunicationsnetwork of claim 82 wherein the values of the average arrival time andthe fractal onset time are used for retrieving the distributed sequencesfrom the memory in conjunction with the Hurst parameter.
 84. Theapparatus for mimicking self-similar traffic in a telecommunicationsnetwork of claim 70 further comprising a blaster unit to generate theselected streams from the self-similar traffic distribution.
 85. Theapparatus for mimicking self-similar traffic in a telecommunicationsnetwork of claim 84 wherein the blaster unit includes the scheduler. 86.The apparatus for mimicking self-similar traffic in a telecommunicationsnetwork of claim 84 further comprising a transmit engine to apply thegenerated streams of self-similar traffic to a portion of atelecommunications network.
 87. A network card comprising the apparatusof claim
 70. 88. A traffic generator comprising the apparatus of claim70.
 89. An apparatus for mimicking self-similar traffic in atelecommunications network, the apparatus comprising a buffer to receivevalues for at least one self-similarity parameter for plural streams,the self-similarity parameters including a Hurst parameter an arbitratorcoupled to the buffer to select at least one of the streams a memorystoring distributed sequences for self-similar traffic correlated to arange of values for the Hurst parameter a distribution calculatorcoupled to the memory, the distribution calculator to generateself-similar traffic distributions for the selected streams based on thevalues of the self similarity parameters for the selected streams,wherein the self-similar traffic distribution is based upon distributedsequences described by a formula having a shape parameter, a minimumvalue for the respective distributed sequences and a uniformlydistributed random variable the shape parameter has a fixed value theminimum value for the distributed sequences is fixed the distributedsequences are obtained from logarithms of values of the uniformlydistributed random variable a scheduler coupled to the distributioncalculator to schedule transmission of data units for the selectedstreams.
 90. The apparatus of claim 89 wherein the memory stores thelogarithms of values of the uniformly distributed random variable, andthe distribution calculator obtains the logarithms from the memory. 91.The apparatus of claim 89 wherein the memory stores the distributedsequences, and the distribution calculator obtains the distributedsequences from the memory.
 92. The apparatus for mimicking self-similartraffic in a telecommunications network of claim 89, wherein thedistributed sequences are Pareto-distributed sequences.
 93. Theapparatus for mimicking self-similar traffic in a telecommunicationsnetwork of claim 89, wherein the distributed sequences aretruncated-value Pareto distributions.
 94. The apparatus for mimickingself-similar traffic in a telecommunications network of claim 89,wherein the distributed sequences comprise competing flows.
 95. Theapparatus for mimicking self-similar traffic in a telecommunicationsnetwork of claim 94 wherein the distributed sequences each comprise asingle ON/OFF process.
 96. The apparatus for mimicking self-similartraffic in a telecommunications network of claim 89, wherein the trafficdistribution comprises a series of ON and OFF periods.
 97. The apparatusfor mimicking self-similar traffic in a telecommunications network ofclaim 96, wherein only one of the ON and OFF periods has a heavy-taileddistribution.
 98. The apparatus for mimicking self-similar traffic in atelecommunications network of claim 97, wherein the heavy-taileddistribution is a Pareto distribution.
 99. The apparatus for mimickingself-similar traffic in a telecommunications network of claim 89 whereinthe distributed sequences comprise superposition of plural independentand probabilistically identical fractal renewal processes.
 100. Theapparatus for mimicking self-similar traffic in a telecommunicationsnetwork of claim 89, wherein the self-similarity parameters include anaverage arrival time and a fractal onset time.
 101. The apparatus formimicking self-similar traffic in a telecommunications network of claim100 wherein the values of the average arrival time and the fractal onsettime are used for retrieving the distributed sequences from the memoryin conjunction with the Hurst parameter.
 102. The apparatus formimicking self-similar traffic in a telecommunications network of claim89 further comprising a blaster unit to generate the selected streamsfrom the self-similar traffic distribution.
 103. The apparatus formimicking self-similar traffic in a telecommunications network of claim102 wherein the blaster unit includes the scheduler.
 104. The apparatusfor mimicking self-similar traffic in a telecommunications network ofclaim 102 further comprising a transmit engine to apply the generatedstreams of self-similar traffic to a portion of a telecommunicationsnetwork.
 105. A network card comprising the apparatus of claim
 89. 106.A traffic generator comprising the apparatus of claim
 89. 107. Acomputer program product comprising a computer usable medium havingcomputer readable program code embodied therein for mimickingself-similar traffic in a telecommunications network, the computerreadable code for causing a processor to receive values for at least oneself-similarity parameter for plural streams, the self-similarityparameters including a Hurst parameter select at least one of thestreams generate a self-similar traffic distribution for the selectedstreams based on the values of the self similarity parameters for theselected streams, wherein the self-similar traffic distribution isfurther based upon distributed sequences retrieved from a table basedupon the value of the Hurst parameter for the selected streams, whereinthe table stores distributed sequences for self-similar traffic. 108.The computer program product of claim 107, wherein the distributedsequences are Pareto-distributed sequences.
 109. The computer programproduct of claim 107, wherein the distributed sequences aretruncated-value Pareto distributions.
 110. The computer program productof claim 107, wherein the distributed sequences comprise competingflows.
 111. The computer program product of claim 110 wherein thedistributed sequences each comprise a single ON/OFF process.
 112. Thecomputer program product of claim 107, wherein the traffic distributioncomprises a series of ON and OFF periods.
 113. The computer programproduct of claim 112, wherein only one of the ON and OFF periods has aheavy-tailed distribution.
 114. The computer program product of claim113, wherein the heavy-tailed distribution is a Pareto distribution.115. The computer program product of claim 107 wherein the distributedsequences are described by a formula having a shape parameter and aminimum value for the respective distributed sequence and a uniformlydistributed random variable.
 116. The computer program product of claim115 wherein the value for the shape parameter is fixed and the minimumvalue for the distributed sequences is fixed.
 117. The computer programproduct of claim 116 wherein the table comprises logarithms of values ofthe uniformly distributed random variable.
 118. The computer programproduct of claim 107 wherein the distributed sequences comprisesuperposition of plural independent and probabilistically identicalfractal renewal processes.
 119. The computer program product of claim107, wherein the self-similarity parameters include an average arrivaltime and a fractal onset time.
 120. The computer program product ofclaim 119, the computer readable code for causing a processor to use thevalues of the average arrival time and the fractal onset time toretrieve the distributed sequences from the table in conjunction withthe Hurst parameter.
 121. A computer program product comprising acomputer usable medium having computer readable program code embodiedtherein for mimicking self-similar traffic in a telecommunicationsnetwork, the computer readable code for causing a processor to receivevalues for at least one self-similarity parameter for plural streams,the self-similarity parameters including a Hurst parameter select atleast one of the streams generate a self-similar traffic distributionfor the selected streams based on the values of the self similarityparameters for the selected streams, wherein the self-similar trafficdistribution is further based upon distributed sequences retrieved froma memory based upon the value of the Hurst parameter for the selectedstreams, wherein the memory stores distributed sequences forself-similar traffic correlated to a range of values for the Hurstparameter.
 122. The computer program product of claim 121, wherein thedistributed sequences are Pareto-distributed sequences.
 123. Thecomputer program product of claim 121, wherein the distributed sequencesare truncated-value Pareto distributions.
 124. The computer programproduct of claim 121, wherein the distributed sequences comprisecompeting flows.
 125. The computer program product of claim 121 whereinthe distributed sequences each comprise a single ON/OFF process. 126.The computer program product of claim 121, wherein the trafficdistribution comprises a series of ON and OFF periods.
 127. The computerprogram product of claim 126, wherein only one of the ON and OFF periodshas a heavy-tailed distribution.
 128. The computer program product ofclaim 127, wherein the heavy-tailed distribution is a Paretodistribution.
 129. The computer program product of claim 121 wherein thedistributed sequences are described by a formula having a shapeparameter and a minimum value for the respective distributed sequenceand a uniformly distributed random variable.
 130. The computer programproduct of claim 129 wherein the value for the shape parameter is fixedand the minimum value for the distributed sequences is fixed.
 131. Thecomputer program product of claim 130 wherein the memory storeslogarithms of values of the uniformly distributed random variable. 132.The computer program product of claim 121 wherein the distributedsequences comprise superposition of plural independent andprobabilistically identical fractal renewal processes.
 133. The computerprogram product of claim 121, wherein the self-similarity parametersinclude an average arrival time and a fractal onset time.
 134. Thecomputer program product of claim 133 wherein the values of the averagearrival time and the fractal onset time are used for retrieving thedistributed sequences from the memory in conjunction with the Hurstparameter.
 135. A computer program product comprising a computer usablemedium having computer readable program code embodied therein formimicking self-similar traffic in a telecommunications network, thecomputer readable code for causing a processor to receive values for atleast one self-similarity parameter for plural streams, theself-similarity parameters including a Hurst parameter select at leastone of the streams generate self-similar traffic distributions for theselected streams based on the values of the self similarity parametersfor the selected streams, wherein the self-similar traffic distributionis based upon distributed sequences described by a formula having ashape parameter, a minimum value for the respective distributedsequences and a uniformly distributed random variable the shapeparameter has a fixed value the minimum value for the distributedsequences is fixed the distributed sequences are obtained fromlogarithms of values of the uniformly distributed random variable. 136.The computer program product of claim 135 further comprising pre-storingthe logarithms of values of the uniformly distributed random variable ina memory in the generating step, obtaining the logarithms from thememory.
 137. The computer program product of claim 135 furthercomprising pre-storing the distributed sequences in a memory in thegenerating step, obtaining the distributed sequences from the memory.138. The computer program product of claim 135, wherein the distributedsequences are Pareto-distributed sequences.
 139. The computer programproduct of claim 135, wherein the distributed sequences aretruncated-value Pareto distributions.
 140. The computer program productof claim 135, wherein the distributed sequences comprise competingflows.
 141. The computer program product of claim 140 wherein thedistributed sequences each comprise a single ON/OFF process.
 142. Thecomputer program product of claim 135, wherein the traffic distributioncomprises a series of ON and OFF periods.
 143. The computer programproduct of claim 142, wherein only one of the ON and OFF periods has aheavy-tailed distribution.
 144. The computer program product of claim143, wherein the heavy-tailed distribution is a Pareto distribution.145. The computer program product of claim 135 wherein the distributedsequences comprise superposition of plural independent andprobabilistically identical fractal renewal processes.
 146. The computerprogram product of claim 135, wherein the self-similarity parametersinclude an average arrival time and a fractal onset time.
 147. Thecomputer program product of claim 146, the computer readable code forcausing a processor to use the values of the average arrival time andthe fractal onset time to retrieve the distributed sequences from thememory in conjunction with the Hurst parameter.